Quantum phase transition in a realistic double-quantum-dot system

Yaakov Kleeorin,Yigal Meir

doi:10.1038/s41598-018-28822-y

Yaakov Kleeorin, Yigal Meir

Open Access

https://doi.org/10.1038/s41598-018-28822-y

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Journal: Scientific Reports	Publication Date: Jul 12, 2018
Citations: 4	License type: open-access

Affiliation: Ben-Gurion University of the Negev

Abstract

Observing quantum phase transitions in mesoscopic systems is a daunting task, thwarted by the difficulty of experimentally varying the magnetic interactions, the typical driving force behind these phase transitions. Here we demonstrate that in realistic coupled double-dot systems, the level energy difference between the two dots, which can be easily tuned experimentally, can drive the system through a phase transition, when its value crosses the difference between the intra- and inter-dot Coulomb repulsion. Using the numerical renormalization group and the semi-analytic slave-boson mean-field theory, we study the nature of this phase transition, and demonstrate, by mapping the Hamiltonian into an even-odd basis, that indeed the competition between the dot level energy difference and the difference in repulsion energies governs the sign and magnitude of the effective magnetic interaction. The observational consequences of this transition are discussed.

Highlights

Quantum phase transitions (QPTs), where a system changes its zero-temperature phase when a physical parameter is continuously varied, is one of the focal research areas in physics in general and condensed matter physics in particular[1,2]
∑ ∑ H2QD = εmnmσ + Umnm↑nm↓ + U12n1n2 mσ m where m = 1, 2 denotes the quantum dots (QDs) index, nmσ = dm†σdmσ, nm = ∑σnmσ, and spin-degeneracy has been assumed
The expectation values and the transmission spectral function see below), required for the evaluation of the conductance through the double dot device[20], were calculated, assuming, for simplicity, equal couplings to the left and right leads, Γ = πρV2, and equal and constant density of states ρ in the two leads, with a symmetric band of bandwidth D around the Fermi energy

Summary

Introduction

Quantum phase transitions (QPTs), where a system changes its zero-temperature phase when a physical parameter is continuously varied, is one of the focal research areas in physics in general and condensed matter physics in particular[1,2]. A transition between singlet and triplet ground states of a single dot can be induced experimentally by a magnetic field[13,14] or by changing the effective potential[15], leading to a crossover from a non-Kondo to a Kondo regime. (Similar setups have already been studied, but with no energy difference between the dots[16] or in the absence of inter-impurity repulsion[17], both of which play an important role in our formulation.) After demonstrating the transition numerically, employing the numerical-renormalization-group (NRG) method, and semi-analytically, using slave-boson mean field theory (SBMFT), we show, by transforming the system Hamiltonian to an even-odd basis, that the difference between the dot energies, relative to the difference between the inter- and intra-dot repulsions, plays the role of a magnetic interaction, which changes its sign, from FM to AFM, at the point where the QPT takes place.

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Results

Conclusion